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Math Help - Help with simplifying?

  1. #1
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    Help with simplifying?

    Rational Equations?



    Last edited by deekay930; December 14th 2009 at 11:05 PM.
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  2. #2
    Super Member Bacterius's Avatar
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    EDIT : I didn't see you posted an image, sorry. But it seems that the link is dead. Can you upload it again ?
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  3. #3
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    Quote Originally Posted by Bacterius View Post
    EDIT : I didn't see you posted an image, sorry. But it seems that the link is dead. Can you upload it again ?
    I fixed it.
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  4. #4
    Super Member Bacterius's Avatar
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    They are not equations but expressions

    For the first one, put them under common denominator (multiply top and bottom of each fraction by the denominator of the other), then factorize. You should find something that simplifies ... look :

    \frac{5}{x + 3} - \frac{x + 2}{x^2 + 4x + 3}

    Factorize the quadratic expression to make it easier first :

    \frac{5}{x + 3} - \frac{x + 2}{(x + 3)(x + 1)}

    Now put under common denominator :

    \frac{5(x + 3)(x + 1)}{(x + 3)(x + 3)(x + 1)} - \frac{(x + 3)(x + 2)}{(x + 3)(x + 3)(x + 1)}

    So it becomes :

    \frac{5(x + 3)(x + 1) - (x + 3)(x + 2)}{(x + 3)(x + 3)(x + 1)}

    Note you can factor out the (x + 3) on the top of the fraction :

    \frac{(x + 3)[5(x + 1) - (x + 2)]}{(x + 3)(x + 3)(x + 1)}

    You can cancel it out :

    \frac{5(x + 1) - (x + 2)}{(x + 3)(x + 1)}

    There may be further simplification possible, though ...

    ---------------------------

    For the second one, you can factor out y^{15} on the top of the fraction, then cancel out :

    \frac{y^{60} + y^{45}}{y^{15}}

    Factor out :

    \frac{y^{15}(y^{45} + y^{30})}{y^{15}}

    Simplify :

    y^{45} + y^{30} with y \neq 0 (keep the domain of the original expression)
    Last edited by Bacterius; December 14th 2009 at 11:27 PM.
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